A316149 Inverse Euler transform of Thue-Morse sequence A001285.

2, -1, -1, 2, -3, 3, 0, -4, 6, -6, 6, -1, -12, 24, -29, 23, 9, -64, 114, -132, 81, 78, -333, 577, -627, 279, 610, -1896, 2979, -2911, 672, 4232, -10754, 15576, -13515, -591, 28098, -61548, 81664, -60408, -27030, 180784, -351081, 425892, -253838, -281760, 1140396, -1995767, 2195952, -930876

Offset

1,1

Links

Seiichi Manyama, Table of n, a(n) for n = 1..5000

N. J. A. Sloane, Transforms

Eric Weisstein's World of Mathematics, Euler Tranceform

Formula

Product_{k>=1} (1-x^k)^(-a(k)) = 1 + Sum_{k>=1} A001285(k)*x^k.

Example

(1-x)^(-2)*(1-x^2)*(1-x^3)*(1-x^4)^(-2)* ... = 1 + 2*x + 2*x^2 + x^3 + 2*x^4 + ... .

Maple

# The function EulerInvTransform is defined in A358451.
a := EulerInvTransform(A001285):
seq(a(n), n = 1..50); # Peter Luschny, Nov 21 2022

Crossrefs

Cf. A001285, A029878.

Sequence in context: A087741 A054991 A302918 * A047071 A124287 A253240

Adjacent sequences: A316146 A316147 A316148 * A316150 A316151 A316152

Keyword

sign

Author

Seiichi Manyama, Jun 25 2018

Status

approved